A generalization of the methods that are currently available to solve systems of ordinary differential equations is made. This generalization is made by constructing linear multistep methods from an arbitrary set of monotone interpolating and approximating functions. Local truncation error estimates as well as stability analysis is given. Specifically, the class of linear multistep methods of the Adams and BDF type are discussed.
","abstract_html":"<p>A generalization of the methods that are currently available to solve systems of ordinary differential equations is made. This generalization is made by constructing linear multistep methods from an arbitrary set of monotone interpolating and approximating functions. Local truncation error estimates as well as stability analysis is given. Specifically, the class of linear multistep methods of the Adams and BDF type are discussed.</p>","abstract_has_math":false,"creators":["Arriola, Leon"],"institution":null,"degree_name":"Doctor of Philosophy (PhD)","degree_level":"Dissertation","degree_discipline":"Mathematics & Statistics","degree_department":null,"school":null,"contributors":["John H. Heinbockel","Robert C. Costen","John Tweed","J. Mark Dorrepaal"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1990,"date_issued":"1990-01-01T08:00:00Z","date_published":"1990-01-01T08:00:00Z","updated_at":"2026-07-24T03:35:08Z","subjects":["Ordinary differential equations","Linear multi-step methods","Nonlinear control theory","Control Theory","Ordinary Differential Equations and Applied Dynamics"],"languages":[],"rights":["In Copyright. URI: http://rightsstatements.org/vocab/InC/1.0/ This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
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"],"dc:subject":["Ordinary differential equations","Linear multi-step methods","Nonlinear control theory","Control Theory","Ordinary Differential Equations and Applied Dynamics"],"dc:title":["A Generalization of Linear Multistep Methods"],"thesis:degree_discipline":["Mathematics & Statistics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Doctor of Philosophy (PhD)"]},"updated_at":"2026-07-24T03:35:08Z"}